When using Extensions > Render > Wireframe Sphere, I get slices (closed shapes with two radii) rather than arcs (unclosed shapes). I found discussions on the dev pages (#3587, #298) which are closed (solved?), but even after re-installing Inkscape I still get this problem.

Thanks for help! 

Are you trying to make a sphere using 'Hide lines behind the sphere' option ? 

If you feel confident making the changes, and have a free editor such as notepad++ ( you have to use a proper text editor  ).

On windows C:\Program Files\Inkscape\share\inkscape\extensions\wireframe_sphere.py

has a couple of lines at the bottom : 

'sodipodi:open': 'true',  # all ellipse sectors we will draw are open
'sodipodi:type': 'arc',

If you add an extraline as below : 

'sodipodi:open': 'true',  # all ellipse sectors we will draw are open
'sodipodi:type': 'arc',
'sodipodi:arc-type': 'arc',

The forum has changed the way I can edit posts, I can't get the spacing correct. 

Python is sensitive to whitespace and will fail if you do not maintain the exact spacing ident to the line above

Sorry the above is to solve the funny lines at the back of the sphere when choosing ''Hide lines behind the sphere' option, does not make the ellipses open though

Looking at the discussions you have linked to they are about bugs in the lines at the back of the sphere ?  The above should solve that.